Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A certain characterstic in a large population has a [#permalink]
08 Sep 2004, 03:39

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

A certain characterstic in a large population has a distribution that is symmetric about the mean M. If 68 percent of the distribution lies within one standard deviation D of the mean, what percent of the distribution is less than M+D?
A. 16% B.32% C. 48% D. 84% E. 92%

Symmetry=> 50% of the distribution lies above the mean (M) and 50% below

If 68% lies within 1 s.d. (D) of M, then 34% lies within +1 D and 34% lies within -1 D.

Thus, the distribution below M+D is the same as the complement of the distribution above M+D, or 1- 0.16 = 0.84.

Alternatively, the distribution below can be found as the sum of the distributions b/w M and +D (34%), M and -D (34%), and below -D (16%), which also sums to 84%.

A certain characterstic in a large population has a distribution that is symmetric about the mean M. If 68 percent of the distribution lies within one standard deviation D of the mean, what percent of the distribution is less than M+D?
A. 16% B.32% C. 48% D. 84% E. 92%

If we could draw a normal bell shaped distribution, we could make the explanation clearer.

In the absence of the normal distribution let me improvise it with this dotted line

A-------- (M-D)----------M------------(M +D)-----------B
In this diagram M is the mean D represents the length of a deviation
This implies that (M-D) to (M+D) represents distribution lying within one standard deviation of the mean and this is 68%
The distribution lying within A to (M-D) and that lying between (M+D) to B must equally account for the remaining 32% (100-68) of the disdtribituion
Thus each of these points will have 16% of the distribution

So we have
A to (M-D) = 16%
(M-D) to M +D =68%
(M+D) to B = 16%

We are intereted in distribution less than (M+D) ie the distribution from A to (M +D) = 16% + 68% = 84%

Thanks everyone. I understand now.
Venksune,
This distribution - 68% , 95% and 99% will hold true only for a normal distribution is it. Is there any other concept similar to this in SD and distributions.
Thanks.

Michigan Ross: Center for Social Impact : The Center for Social Impact provides leaders with practical skills and insight to tackle complex social challenges and catalyze a career in...

The Importance of Financial Regulation : Before immersing in the technical details of valuing stocks, bonds, derivatives and companies, I always told my students that the financial system is...

The following pictures perfectly describe what I’ve been up to these days. MBA is an extremely valuable tool in your career, no doubt, just that it is also...